Havener had back-to-back baskets to break an 11-all tie and give BU (7-6) the lead for good. The Terriers led 39-18 halftime after the Division III Cougars (1-9) made just 6 of 21 shots, including four 3-pointers. Kean didn't get closer than 20 in the second half.
The Terriers, who shot 52 percent, were 12 of 28 from 3-point range, running their streak of making at least one trey to 600 games dating to 1996.
Tom Soulias scored 19 points for Kean.
The victory was the fourth in five games for BU, which begins Patriot League play Wednesday at Holy Cross.